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Page "Algebraic number" ¶ 20
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One and may
One can see it as humiliating that an extra hormone casually fed into our chemistry may induce us to lay down our lives for a lover or a friend ; ;
One might, indeed, argue that the history of ideas, in so far as it includes the literatures, must center on characterizations of human nature and that the great periods of literary achievement may be distinguished from one another by reference to the images of human nature that they succeed in fashioning.
One may be exasperatingly aware that if the answer is favorable it will be judged such only by those of one's own age.
One may be sure the present Republican congressional leadership hasn't meant to repeat this error.
One may conclude that most of the detected micrometeoritic material is concentrated in orbital streams which intersect the Earth's orbit.
Justices Frankfurter and Jackson dissented: `` One State may cherish formalities more than another, one State may be more responsive than another to procedural reforms.
One upward-mobile teacher may be a hard taskmaster for lower-class pupils because she wants them to develop the attitudes and skills that will enable them to climb, while another upward-mobile teacher may be a very permissive person with lower-class pupils because he knows their disadvantages and deprivations at home, and he hopes to encourage them by friendly treatment.
One sitter may think `` a leather couch '' identifies a reading as surely directed to him ; ;
One might say, " Even though the usual ordering of the real numbers does not work, it may be possible to find a different ordering of the real numbers which is a well-ordering.
One may also acquire Tasbih and recite the names of Allah in such manner as " SubahannAllah " or Glory be to Allah in Arabic over and over again to acquire good deeds.
One may try to quantize an electron field without mixing the annihilation and creation operators by writing
Such an anagram may be a synonym or antonym of its subject, a parody, a criticism, or praise ; e. g. George Bush = He bugs Gore ; Madonna Louise Ciccone = Occasional nude income or One cool dance musician ; William Shakespeare = I am a weakish speller, Roger Meddows Taylor = Great words or melody.
One may distinguish between this positional system, which is identical throughout the family, and the precise glyphs used to write the numerals, which vary regionally.
One may also encounter chitronchelo or ( in Italian ) citroncello, based on lemon.
* One of the more serious of these side effects is tardive dyskinesia, in which the sufferer may show repetitive, involuntary, purposeless movements ( that are permanent and have no cure ) often of the lips, face, legs, or torso.
One study has suggested that cannabidiol may be as effective as atypical antipsychotics in treating schizophrenia.
One paper has found that alcohol use at an early age may influence the expression of genes which increase the risk of alcohol dependence.
One popular technique is to mock external interfaces or data to mimic other stories which might not be played out during an iteration ( as those stories may have been relatively lower business priority ).
One master may communicate with up to 7 slaves in a piconet ; all devices share the master's clock.
One can also consider partial binary functions, which may be defined only for certain values of the inputs.
One property many proteins have is that they specifically bind to a certain molecule or class of molecules — they may be extremely selective in what they bind.

One and generalize
One can generalize the concept of Cartesian coordinates to allow axes that are not perpendicular to each other, and / or different units along each axis.
One can generalize the above example to arbitrary limits and colimits.
One can generalize to formal power series in more than one indeterminate, to encode information about arrays of numbers indexed by several natural numbers.
One may generalize this notion by replacing the field of scalars by a commutative ring, and thus defining an algebra over a ring.
One can generalize further by allowing the entries to lie in a ring, rather than in a field.
One can generalize the Wightman axioms to dimensions other than 4.
One representation, called AnalogySpace, uses singular value decomposition to generalize and represent patterns in the knowledge in
# One cannot generalize on the basis of an individual case and, therefore, the case study cannot contribute to scientific development.
) One crucial limitation to the full credibility of Waldinger's study, however, is that it is based entirely on research in New York City and, therefore, its findings are difficult to generalize to cities like Detroit, Baltimore, Philadelphia, Cleveland, and others where blacks were indeed concentrated in the manufacturing sector.
One can generalize this principle to an arbitrary number of data fields associated with a single record, with each field representing a different aspect of a fact or bundle of facts.
One can easily generalize the definition of superalgebras to include superalgebras over a commutative superring.
One can generalize Alexander's construction to generate other horned spheres by increasing the number of horns at each stage of Alexander's construction or considering the analogous construction in higher dimensions.
One may generalize this setup, allowing the algebra to be noncommutative.
One can generalize this concept to more dimensions and other kinds of curved surfaces which makes it useful in various kinds of simulations.

One and numbers
One of the simplest algorithms is to find the largest number in an ( unsorted ) list of numbers.
One must be careful here ; for instance, some analyses count an addition of two numbers as one step.
One can define for all natural numbers k at once by the relation
One of the first proposed estimates of the total number of beetle species on the planet is based on field data rather than on catalog numbers.
One way to visualize this identification with the real numbers as usually viewed is that the equivalence class consisting of those Cauchy sequences of rational numbers that " ought " to have a given real limit is identified with that real number.
One may also wish to talk about definable complex numbers: complex numbers which are uniquely defined by a logical formula.
One lemma states that the difference of the cubes of two rational numbers is equal to the sum of the cubes of two other rational numbers, i. e. given any a and b, with a > b, there exist c and d, all positive and rational, such that
One point agreed on is that fractal patterns are characterized by fractal dimensions, but whereas these numbers quantify complexity ( i. e., changing detail with changing scale ), they neither uniquely describe nor specify details of how to construct particular fractal patterns.
One way to find that analytic continuation is to use Euler's integral for positive arguments and extend the domain to negative numbers by repeated application of the recurrence formula,
One way to avoid the use of large numbers is by declaring a new unit of currency ( an example being, instead of 10, 000, 000, 000 Dollars, a bank might set 1 new dollar = 1, 000, 000, 000 old dollars, so the new note would read " 10 new dollars.
One of only two American cycle manufacturers to survive the Great Depression, Harley-Davidson again produced large numbers of motorcycles for the US Army in World War II and resumed civilian production afterwards, producing a range of large V-twin motorcycles that were successful both on racetracks and for private buyers.
One of the binary numbers to be multiplied is represented as a trivial polynomial, where, ( using the above notation ): a < sub > i </ sub >
One of his most famous numbers is " They Ain't Makin ' Jews Like Jesus Anymore ," a song in which Kinky verbally and physically beats up a drunken white racist who berates blacks, Jews, Greeks, and Sigma Nus in a bar.
One begins by listing all of the numbers vertically in a table ( in this example 4, 7, 12, 21, and 42 ):
One of the most familiar groups is the set of integers Z which consists of the numbers
One of the reasons M-theory is so difficult to formulate is that the numbers of different types of membranes in the various dimensions increases exponentially.
One way to prove that a class is proper is to place it in bijection with the class of all ordinal numbers.
One may also study real numbers in relation to rational numbers, e. g., as approximated by the latter ( diophantine approximation ).

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